A Survey of Binary Covering Arrays

Binary covering arrays of strength $t$ are 0–1 matrices having the property that for each $t$ columns and each of the possible $2^t$ sequences of $t$ 0's and 1's, there exists a row having that sequence in that set of $t$ columns. Covering arrays are an important tool in certain applications, for example, in software testing. In these applications, the number of columns of the matrix is dictated by the application, and it is desirable to have a covering array with a small number of rows. Here we survey some of what is known about the existence of binary covering arrays and methods of producing them, including both explicit constructions and search techniques.